cut is a strange word in that it doesn't change tense in these types of sentences, The context/other words tells you the tense, in your sentence it is past tense, because you have had ( past tense) it cut. But I can also say, Tomorrow I will get my hair cut. so here it is in future tense....I'm at the hairdressers getting my hair cut..present tense.
It would change tense if you were the person doing the cutting though ie: I cut his hair- past tense, I am cutting his hair-present tense
I would try not to worry about getting your head round causative verb form...I'm English and I don't even know what that means. lol. Learning a language should be about doing, and learning by context etc, leave the fancy grammar terms to the professional linguists, you will only get confused! Just like I was by the first part Brad's answer, no offence Brad, Im sure what you said is correct and true, I just think its better to try and keep things simple!